Impedance Matching

Part of Telephony

The technique of equalizing source and load impedance to maximize power transfer in telephone circuits.

Why This Matters

Impedance matching is one of the most important and least intuitive concepts in electrical engineering. The maximum power transfer theorem states that a source delivers maximum power to a load when the load impedance equals the source impedance. Mismatched impedances waste power, reduce signal levels, cause reflections on transmission lines, and degrade audio quality. Understanding impedance matching explains why telephone circuits use specific standard impedances, why transformers are ubiquitous in audio equipment, and why cable impedance specifications exist.

In practical telephone work, you encounter impedance matching decisions constantly: coupling a microphone to a line, connecting a receiver to a long cable, building a hybrid (four-wire to two-wire conversion), or interfacing with exchange equipment built to a different impedance standard. Making the wrong impedance decisions results in telephone systems that work poorly despite technically correct component selection.

Impedance Concepts

Impedance extends the concept of resistance to AC circuits. Resistance opposes current in proportion to current magnitude. Reactance (the AC counterpart of resistance) opposes changes in current — capacitors have capacitive reactance that decreases with frequency, inductors have inductive reactance that increases with frequency. Impedance combines both: Z = R + jX where j indicates the imaginary (reactive) component.

For audio circuits, impedance varies with frequency. A telephone line at 1,000 Hz has different impedance than the same line at 3,000 Hz because the line’s capacitance (distributed along its length) has different reactance at different frequencies. This frequency-dependence means impedance matching for the full telephone audio band is a design compromise — you optimize for the mid-band frequency and accept some mismatch at the extremes.

The standard telephone impedance in North America is 600 ohms (resistive). European standards have historically used 600 ohms but also 150 ohms for some equipment. This standard allows equipment from different manufacturers to interconnect correctly without per-connection impedance measurement.

Transformer Matching

The transformer is the primary tool for impedance matching. A transformer with a turns ratio of n:1 transforms impedance by n²:1. A transformer with a 10:1 turns ratio transforms a 60,000-ohm source impedance to 600 ohms at the secondary.

This works because transformer voltage scales with turns ratio but current scales inversely. If voltage is multiplied by n and current is divided by n, the apparent resistance (V/I = voltage/current) scales by n/n⁻¹ = n². The load sees a different impedance than the source impedance, but from the source’s perspective, the load plus transformer appears as the source’s own impedance.

For telephone microphone coupling, a carbon microphone with DC operating resistance of ~150 ohms must drive a 600-ohm line. A transformer with a turns ratio of 2:1 (impedance ratio 4:1) transforms the 150-ohm source to 600 ohms at the secondary — but note that for a carbon microphone, the operating principle is different; the microphone modulates current rather than generating voltage, so the transformer analysis is more complex and involves the line battery as well.

For electromagnetic microphones (dynamic type) with typical source impedance of 150-300 ohms driving a 600-ohm line, a 1:2 step-up transformer (impedance ratio 1:4) matches the source to load correctly.

Practical 600-Ohm Standards

The 600-ohm standard came from the characteristic impedance of standard twisted-pair telephone cable at voice frequencies. By standardizing all equipment interfaces at 600 ohms, Bell System engineers ensured that any equipment combination would interface correctly without transformer calculation.

In practice, 600 ohms is maintained at junction points — between telephone instruments and lines, between lines and exchange equipment, between trunk circuits at different exchanges. Internal circuit impedances within an instrument may be quite different; the 600-ohm requirement applies at the external interface points.

Testing impedance matching: connect a signal generator through a 600-ohm source resistance to the circuit under test. Measure voltage across the 600-ohm source resistance and across the circuit’s terminal. For a matched 600-ohm load, both voltages are equal (voltage divider, equal resistances). If the load shows significantly lower voltage, it presents impedance below 600 ohms. If it shows higher voltage, it presents impedance above 600 ohms.

Bridging Connections

A bridging connection (high-impedance tap on a circuit) allows monitoring a circuit without significantly loading it. The monitoring device’s input impedance must be much higher than the circuit impedance — typically 10x or more. A 600-ohm circuit can be bridged by an instrument with 6,000 ohms or more input impedance with less than 1 dB insertion loss.

This principle allows subscriber line test equipment to be connected in-service without interrupting the call — the high-impedance test set bridges the 600-ohm line and monitors without disturbing the active conversation.

Reflection and Line Matching

For telephone signals traveling down transmission lines, impedance mismatch at the termination causes reflections — a fraction of the signal bounces back toward the source. In short local loops (under a few kilometers), reflections at voice frequencies are negligible because wavelengths are many thousands of kilometers long. However, in broadband circuits (ADSL, carrier telephone systems), reflections cause serious degradation and proper termination becomes essential.

For voice-grade telephone circuits, terminate each line end in its characteristic impedance (600 ohms for standard pairs) to absorb the signal cleanly rather than reflecting it. An exchange line interface includes a 600-ohm termination to absorb any signal arriving from the subscriber loop and prevent it from reflecting back into the exchange equipment.